Last updated 20211015
Please direct inquiries to Christie Chiu, cschiu@princeton.edu.

Included in this database are two files, materials.tsv and lattices.csv, containing the data 
from C.S. Chiu, A.N. Carroll, N. Regnault, and A.A. Houck. Line-graph-lattice crystal structures of 
stoichiometric materials, (2021).

The first file, materials.tsv, tabulates the ICSDs from the Flatband Materials Database that 
have been identified to have line-graph-lattice crystalline structures. Each row is an ICSD 
with its derived lattice, and the columns are as follows:
- ICSD: 			ID from the Inorganic Crystal Structure Database
- SG: 			space group of the ICSD
- bond cutoff [Ang]: 	cutoff distance below for bonds between atoms with hopping amplitude 1;
			there is no hopping between atoms which are farther apart than the 
			cutoff. Cutoff parameter determination is detailed in Appendix A of the 
			paper. Units are Angstroms.
- dim:			dimension of the lattice (2D, q2D, or 3D)
- Miller plane:		Miller plane along which the 2D lattice resides, for 2D lattices only
- non-kagome/non-pyrochlore-like:	boolean indicating whether the lattice is non-kagome or 
				non-pyrochlore-like (1 = True, 0 = False/kagome/
				pyrochlore-like)
- gap [t]:		gap between the flat (lowest) bands and the first dispersive band, under
			the tight-binding model, in units of the tunneling amplitude (here set 
			to 1). Estimated uncertainties <0.001
- fb degeneracy:		degeneracy of the flat (lowest) band.
- S-matrix compatible:	boolean indicating whether the lattice is compatible with the S-matrix 
			method, see manuscript for details.
- lattice #:		ID number of line-graph lattice this material corresponds to
- atoms + positions:	list of lattice sites (vertices), numbered; atomic element; direct 
			coordinates
- adjacency list:	list of adjacencies, in the format (vertex1, vertex2, (unit cell vector
			between vertices))
Note that because multiple bond cutoffs are tested for each ICSD, some ICSDs may be 
represented more than once. In this case, the discrete bond cutoffs yield discrete lattice 
structures.

The second file, lattices.csv, tabulates the unique line-graph lattices detected during our 
search. Each row indicates a lattice geometry, and the columns are as follows:
- #:			the ID number for the lattice. Begins with the lattice dimension (q2D 
			grouped in with 3D lattices)
- lattice frequency:	the number of ICSD-cutoff instances which have this lattice 
			structure
- dim:			dimension of the lattice geometry (2D, q2D, 3D)
- non-kagome/non-pyrochlore-like:	boolean indicating whether the lattice is regarded as being 
				not kagome or pyrochlore-like. Note that for the lattices 
				which are pyrochlore-like, there may be some lattice 
				geometries which are not isomorphic to the pyrochlore 
				lattices, but are sufficiently similar that we cannot 
				distinguish between them in our high-throughput algorithm.
- gap:			boolean indicating whether the flat (lowest) bands are gapped from the
			first dispersive band, under the tight-binding model.
- fb degeneracy:		degeneracy of the flat (lowest) band, normalized by the reduction factor
			described in 'clique size ratios'.
- S-matrix compatible: 	boolean indicating whether the lattice is compatible with the S-matrix 
			method, see manuscript for details.
- 'clique size ratios':	sizes and frequencies of the cliques represented in the lattice, where 
			frequencies are reduced such that their greatest common factor is 1. 
			This is done to account for lattices which may have a unit cell given by 
			multiple copies of the unit cell of another lattice. All other 
			frequencies in the metrics below are also scaled by this reduction 
			factor. Denoted as a list of 'size(frequency)' pairs.
- 'clique pair ratios':	sizes and frequencies of the pair of cliques around each vertex of the 
			lattice. As some vertices are only in one clique, there will be lists of 
			single clique sizes. Denoted as a list of '[size1 size2](frequency)' 
			pairs.
- 'face size ratios':	sizes and frequencies of the faces of the lattice, for 2D lattices. 
			Denoted as a list of 'size(frequency)' pairs. As faces are not 
			well-defined for the quasi-2D and 3D lattices, this is not included for 
			lattices of those dimensions.
- 'face pair ratios':	sizes and frequencies of the pair of faces around each vertex of the 
			lattice, for 2D lattices only. As some vertices only border one face, 
			and some zero (e.g. those in within the outer bounds of a clique), there 
			will be empty lists and lists with single face sizes. Denoted as a list 
			of '[size1 size2](frequency)' pairs.
- 'cliques around faces':	sizes of the cliques encircling each face of the lattice, for 2D 
			lattices only. Denoted as a list of '[size1 ...sizen](frequency)' 
			pairs, where the number of clique sizes in each is given by the face 
			size.